ABSTRACT
When considering an infinite sequence (of points, numbers, or functions) contained in a space, we would like the limit of the sequence to be contained in the same space. In other words, a space is desired to be complete.1 This is because completeness of a given space guarantees the existence of the limit in the space; as a result of the fact, we are able to establish a self-consistent theory based on the infinite sequence contained in the space.
